I am interested in module theory mainly in connection with commutative algebra. I would like to know what are the main areas of research in this field and who are the researchers more active in it. I am asking this question because I want to do research in the area.
To improve the question, for example I would like to know what are the relevant papers about prime submodules.
I recommend searching through the arxiv for any papers relating to prime module theory. Most mathematicians who work with modules use them for their research in Algebraic Geometry, Homological Algebra, Commutative Algebra, Representation Theory and almost any other Algebra heavy field.